The second of the judges' visits to projects longlisted for the Art Fund museums prize was to the Yorkshire Museum. I have to admit a special interest here: I am writing a book on Roman Britain (to be published by Jonathan Cape; but don't hold your breath) and had been looking forward to seeing the Roman collection here for ages. I was not disappointed: it is stupendous. Fantastic inscribed family tombs; an imposing sculpture of the god Mars (the first thing you see as you come through the front door); the last epigraphic reference to the Ninth Legion before they disappear from history (leaving a trail of mystery behind them) and, astonishingly, a Roman bun – I'm talking a hairdo rather than a species of cake – complete with its original hair pin. Fellow judge Kathy Gee said that growing up in York and visiting the museum as a child, this was the object that she had, above all others, found compelling. I found it pretty unsettling, too.

But the point of the trip was not to salivate over its collection (though you should see the dinosaur fossils... the perfectly preserved Saxon helmet with its Latin inscriptions... the profoundly dignified medieval sculptures... the exquisite craftsmanship of the Middleham jewel, a 15th-century golden pendant set with a sapphire), but rather to admire its redevelopment – which, to revamp and redisplay the whole museum, had cost a mere £2.2m.

Yorkshire Museum staff member Martin Watts in the library (the stuffed bear is visible in the background). Photograph: Jeremy Deller

Yorkshire Museum is the second-oldest purpose-built museum in the UK, built by the Yorkshire Philosophical Society in the 1830s. It is a properly a building of the enlightenment: all Greek columns, skylit double-height galleries, and a wonderful library with old wooden bookcases, dusty 19th-century volumes and (oddly) a stuffed bear in a glass case sporting a top hat. However, before its redevelopment, the building had very little opportunity to breathe. All its windows were blocked up. The double-height galleries had been fitted with false ceilings. Extra plywood walls had been put in. Visitors would apparently describe their visits as "draining".

Chairman of the judges Michael Portillo at the Yorkshire Museum. Photograph: Jeremy Deller

The curators of the museum decided that what they urgently needed to do was open the museum up and rediscover its elegance and beauty. This they did – using their bare hands. Andrew Morrison, head curator, gave a vivid description of how he and his colleagues pulled down false ceilings, filled 83 skips with rubbish, learned how to plaster walls. "I even found a Roman sculpture we didn't know we had," he said (it had been hidden behind a wall hastily erected last century). They had the chief executive vacuuming floors, while the museum technician suddenly became the most important person around the place as his practical expertise came to the fore. Volunteers were set to work dusting medieval sculptures. If the staff could manage a task themselves, they just rolled up their sleeves and did it – even to the extent of shifting an entire Roman fresco. A contractor offered to do that job for £13,000; they did it themselves with the help of volunteers "so it cost us an afternoon's cake".

It really was an inspiring lesson in what you can achieve with very little money – and a great deal of Yorkshire grit.